I don't like recent file lists, either. (Not in any application, not even a word processor.) TweakUI for XP does have the ability to scrub the recent file lists for many parts and applets of the OS, but I don't think it covers the WMP.
I've noticed that, if you play files by double-clicking on them in Windows Explorer, the filenames don't show up in the list.
I've seen the below reg file posted in lots of places. It would appear to blow away the recent file lists for WMP. I've never tested it because I primarily use WMP for playing back DVDs. I only play media files off the hard drive by double-clickin on them in Windows Explorer, as I mentioned before.
--------------- file begins after this line -----------------
REGEDIT4
[-HKEY_USERS\.Default\Software\Microsoft\MediaPlayer\Player\RecentFileList]
[-HKEY_CURRENT_USER\Software\Microsoft\MediaPlayer\Player\RecentFileList
--------------- file ends before this line -----------------
- Collin